Howbeit on the tenth day of this seventh month is the day of atonement; there shall be a holy convocation unto you, and ye shall afflict your souls; and ye shall bring an offering made by fire unto the Lord.

— Leviticus 23:27

When it began:

Yom Kippur is considered the date on which Moshe (Moses) received the second set of Ten Commandments. It occurred following the completion of the second 40 days of instructions from God. At this same time, the Israelites were granted atonement for the sin of the Golden Calf; hence, its designation as the Day of Atonement.

How it’s observed today:

Yom Kippur is the absolute holiest day of the year for the Jewish people, its central themes being repentance and atonement. It is an approximate 25-hour period of fasting and intensive prayer, with the majority of the day often spent in the synagogue. Unlike regular days, which have three prayer services, Yom Kippur service has five prayer services: 1) Maariv, with its solemn Kol Nidrei service, on the eve of Yom Kippur; 2) Shacharit, the morning prayer; 3) Musaf, which includes a detailed account of the Yom Kippur Temple Atonement Service; 4) Mincha, which includes the reading of the Book of Jonah. Finally, in the waning hours of the day, we reach the climax of the day: the fifth prayer, the Neilah (“locking”) prayer. The gates of heaven, which were open all day, will now be closed, with us on the inside. During this prayer we have the ability to access the most essential level of our soul. The Holy Ark remains open throughout. The closing Neilah service climaxes in the resounding cries of “Hear O Israel . . . God is one.” Then joy erupts in song and dance, followed by a single blast of the shofar, and the proclamation, “Next year in Jerusalem.”

On Yom Kippur, the Torah instructs us to "afflict" ourselves, which means abstaining from an assortment of physical pleasures. There are two reasons for this: a) on this day, when our connection to God is brought to the fore, we are compared to angels, who have no physical needs. b) We afflict ourselves to demonstrate the extent of our regret for our past misdeeds.

There are five areas of pleasure that we avoid on Yom Kippur:

Eating or drinking.

Wearing leather footwear.

Bathing or washing.

Applying ointment, lotion, or creams.

Engaging in any form of spousal intimacy.

Customs:

Prior to the fast, eating a festive meal, giving charity and asking others for forgiveness.

Wearing white garments on Yom Kippur, symbolizing our desire to be like the angels: lighter, clean, pure and transparent. Additionally, wearing white is a reminder of the white burial shrouds Jews are buried in. The reminder that we all stand at the edge of death is a powerful motivator to review our lives and make amends.

It is customary not to wear gold jewelry on Yom Kippur, as gold is reminiscent of the sin of the Golden Calf, and on the Day of Atonement, the day when we were forgiven for that egregious sin ,we do not want to "remind" the Prosecutor (Satan) of our past sins.

Many people have the practice of bringing a lemon to the synagogue often with cloves thrust into it. They smell the lemon occasionally over the course of Yom Kippur and recite the blessing that is said over spices of Borei Minei Besamim. This is to fulfill the rabbinical dictate of reciting 100 blessings a day, a somewhat challenging endeavor on a fast day when we don’t eat and therefore don’t recite the before and after blessings on food.

After the fast, we partake of a festive after-fast meal, affirming the faith that we’ve been forgiven and we have a clean slate, making the evening after Yom Kippur a (festival) in its own right.